Page size
If you need a site to work on a 56kbps connection you need to go as "close to bare metal" as you can.
By that I mean no libraries or frameworks (no bootstrap, React, Angular etc. etc. and definitely no themes from places like themeforest, those things are always bloated!), just vanilla JS, CSS and HTML.
No custom fonts either I am afraid, they add loads of weight, instead use a web safe font combination
You probably want the total page weight to be under 100kb and ideally under 50kb.
Image
With regards to images you should use WebP if the browser supports it and fall back to jpeg. I would compress images to 70% (as a nice balance between quality and size).
It doesn't matter what format they supply it to you you should convert it.
Also make sure images are sized correctly (so if they display at 400px by 250px make sure the image is 400px by 250px so you aren't sending any wasted bytes).
Even better if you can use SVG for images (company logos tend to be SVG etc.) as those are likely to be even smaller and will scale to any screen size without loss of quality. If they give you SVGs then use them.
Other basic things to consider
Try to keep requests as low as possible, 56kbps connections tend to have huge latency so the round trip time for requests can seriously impact performance. Try to keep total requests under 20 (and ideally under 8!).
Hopefully the above should get you started. If you want to learn more about performance I would suggest heading over to Stack Overflow and looking at the "pagespeed-insights" tag as that is nearly all related to speed.
Finally using Page Speed Insights / Lighthouse in developer tools in Chrome browser (F12 -> Lighthouse) as you build the site will help you see if you have the page loading quick. You really need to try and get above 95 for someone on a 56kbps connection to have a chance.
